The 100% fixed rule of thumb with field of view is that lowering the magnification increases a scope's field of view. Comparing scopes' specs of a 1" to a 30mm tube scope at the same lowest magnification on the scope manufacturer's website, the field of view is usually equal. But you will find that with some scopes, the 30mm has a bigger FOV while some 1" tube scopes can have a bigger FOV. Who knows why?! What about a better sight picture? From Swarovski's website, "With a 30mm tube, the internal lenses can be made slightly larger, which increases optical performance simply because larger lenses always perform better than smaller ones, all else being equal." A 30mm tube can dictate a larger ocular housing being used which then can translate to a wider FOV, and that depends on the internal construction. Hence, the strange variation in FOV. So you are both right. By far the biggest advantage of a bigger tube is the increase in elevation adjustment range, e.g. a scope with a 30mm tube has a 75% greater adjustment range than a 1" tube scope. When I worked in optics, that is what I told customers. For long range shooting over 1,000 yards, a 30, 34, 35 or 40mm tube offers a significant advantage.
FOV is constrained by many things, and of course, magnification is among the most important factors. Another critical factor is ID of the erector tube, because ultimately that is what is being transmitted to the eyepiece.
A 30mm tube usually has about 4mm more play inside compared to a 1inch tube. So, yes, you can have bigger lens OR more adjustment range; not both. I do believe that most riflescope with 30 mm tube have the same size erector lenses as the ones in 1 inch tubes and they thus offer greater adjustment range. Also a 30mm tube is stronger than a 1inch tube with the same wall thickness, simply because its bigger.
Now if the manufacturer decided to forego the extra adjustment range and instead opted for bigger internal lenses, then we would have an extra 4mm to play with. This would provide a wider field of view right at the start because the erector tube would be wider. I have no clue how big the internal lenses are but 4mm would indeed allow more light through since bigger lenses admit more light.
I always look at the adjustment range to see if it's significantly larger in a 30mm tube compared to a 1inch tube. If it is, I now know the erector tube is the same, so same FOV and brightness as the 1inch tube.
When I got my first March, I thought the 34mm tube provided for additional adjustment range or bigger internal lenses compared to a 30mm tube. I was wrong, it was neither one of those. The wall thickness went from 2mm to 4mm and that accounted for the 30mm to 34mm increase.
I believe the 40mm tubes actually have larger internal lenses compared to 30/34/35mm tubes.
Of course, there are other tricks used to increase the adjustment range and the FOV, but that's for another day.
For now, let's just say that in most cases the 30mm tubes do not offer greater FOV and brightness comapre to 1inch tube; they usually use the extra space for greater adjustment range and that makes a lot of sense.